A wide variety of products have been developed to assist students in learning fundamental arithmetic and mathematical concepts. For example, many products are configured to teach concepts such as counting or number sense, place value and the arithmetic operations of addition, subtraction, multiplication and division. Such products often include components such as counting pieces configured to be arranged geometrically and instruction sheets containing information regarding how the products can be used to teach certain mathematical concepts. For example, the “base ten blocks” system is an exemplary mathematics education system. The base ten blocks system comprises four sizes of counting pieces (ones, tens, hundreds and thousands), each representing a power of ten. The counting piece representing ones is a small cube; the counting piece representing tens is an elongated rod having the length of ten ones; the counting piece representing hundreds is a square having the area of ten tens; and the counting piece representing thousands is a large cube having the volume of ten hundreds. These counting pieces, which can be configured to connect to one another, help the student to understand the relationship between various base ten numbers, and thereby teach the concept of place value.
Another exemplary mathematics education system is the “number rods” system. This system comprises a series of colored rods of various lengths representing the numbers one through ten. Number rods can be used to teach addition and subtraction by having the student compare the rods corresponding to the numbers of interest. For example, the rod representing the number 2 and the rod representing the number 3 can be aligned and placed alongside the rod representing the number 5 to illustrate a basic “math fact” such as 2+3=5, or 5−2=3. In some embodiments, a number rods system further comprises one or more linear, separate, numbered tracks, each consisting of a single row, that are labeled with numbers to assist the student in performing arithmetic functions and learning math facts.
Basic math facts can also be taught using a “hundreds board” system. Hundreds boards generally consist of a flat board with a 10×10 grid (some teachers just use a photocopied sheet). In the grid are the numbers 1 through 100, starting at one in the upper left, proceeding across the first row to 10, repeating starting on the next row 11–20, and so on. The grid and numbers may simply be printed on, or the board may be configured so that the individual squares can hold tiles or other objects. The boards often come with individual tiles that can be placed on top of individual numbers on the board. The board is useful for counting and teaching basic math facts. To add 15+18, a student would typically count to 15, place down a tile or object, and then count out 18 from that point and place a second tile on the sum of 33. Disadvantageously, the hundreds board tends to reinforce counting-based arithmetic, which is precisely what advocates of base ten-oriented teaching are trying to discourage. A conventional hundreds board also does not allow students to manipulate the numbers 1–10 in the framework or easily perform arithmetic operations.